Wetting effect and morphological stability in growth of short-period strained multilayers

Abstract

We explore the morphological stability during the growth of strained multilayer structures in a dynamical model which describes the coupling of elastic fields, wetting effect, and deposition process. We quantitatively show the significant influence of the wetting effect on the stability properties, in particular for short-period multilayers. Our results are qualitatively similar to recent experimental observations in AlAs/InAs/InP(001) system. We also give predictions for strainbalanced multilayers.Strained periodic multilayer films composed of different material layers have attracted much attention since such material structures can have tunable electronic properties. Among the actively investigated systems is the multilayer with alternating tensile/compressive layers coherently grown on a substrate, resulting in a modulated structure like short-period superlattice [e.g., GaAs/InAs 1 or AlAs/InAs 2,3,4 on InP(001)] or a multiple quantum well [e.g., GaInP/InAsP on InP(001)] 5 . Generally morphological instability occurs in such coherent lattice-mismatch multilayer structures, driven by a gradual release of misfit-generated stresses when dislocations are absent. Consequently, undulations are observed in the strained layers, instead of ideally flat interfaces. This stress-driven morphological instability can lead to lateral compositional modulations in vertical short-period superlattices, 1,2,3,4 as a result of layer thickness modulations (caused by interface rippling) and different material components in adjacent layers. 3,5 The spontaneous formation of these lateral modulations is also a promising way to self-organize fabrication of low-dimensional quantum heterostructures, especially quantum wires. 1,2,3 Although understanding of the detailed growth mechanism in multilayer structures is important and of much interest for both fundamental studies and device applications, it is still far from complete due to the complexity of the system. This complexity arises from the coupling of strain fields in different layers, and the nonequilibrium nature of the growing film for which material deposition rates play an important role in the pattern formation. Previous theoretical analyses use some approximations to determine the elastic fields, treating each buried island 6 or nonplanar interface 7 of the multilayer as a misfitting inclusion in a semi-infinite homogeneous medium. Recently, a general method has been developed to directly calculate the elastic state of the multilayer system. 8 Wetting effects have been considered in the context of single-layer strained film growth, 9,10 but not for multilayers. In this letter, we attempt to remedy this. The wetting effect arises from the change of material properties across interlayer interfaces within the system, and is especially important for thin composite layers. Here, we incorporate the wetting effect (arising from nonlinear elastic contributions 10 ) in the early morphological evolution of growing multilayer films. We focus on the stability properties of the system and o...

Phase-field-crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures

“…In the following we provide an alternative derivation procedure for PFC dynamics, including two steps: i) directly use the original free energy functional (17) and the DDFT equations (15) to obtain the expressions of ∂ρ A(B) /∂t, and then ii) derive the dynamics of n and ψ through Eq. (25), instead of using Eqs.…”

“…where ∆ρ A l = ρ A l /ρ l and ∆ρ B l = ρ B l /ρ l . From the DDFT equations (15) we can obtain the PFC equations for A & B components respectively, i.e.,…”

“…However, the limitation of small length and time scales addressed in these atomistic methods leads to large computational demands and hence the restriction of system size and evolution time range that can be accessed. Such limitation can be overcome via continuum modeling methods, including continuum elasticity theory used in strained film growth [5,[11][12][13][14][15][16][17] and the well-known phase field models that have been applied to a wide range of areas such as crystal growth, nucleation, phase separation, solidification, defect dynamics, etc. [18][19][20][21][22].…”

Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude-equation analysis of the phase-field-crystal model

“…Surface energy is known to play a stabilization role on film evolution and for simplicity is often approximated as misfit independent in many strained film studies. [8][9][10][19][20][21][22][23][24][25][26][27][28][29] However in the presence of a strain field, the surface energy is known to vary as a result of intrinsic surface stress σ 0 and is usually expanded up to 2nd order in terms of strain tensor u ij (with i, j the film surface coordinate indices) in linear elasticity (in the coexisting liquid and solid regions respectively) as a function of misfit strain εm, with parameters the same as those of Fig. 3.…”

“…Quantitative results have been obtained to reveal fundamental mechanisms of film nanostructure formation observed in a variety of experimental systems. Recent work has focused on morphological instabilities of strained films [8][9][10] or superlattices, [22][23][24] the coupling to alloy film composition inhomogeneity, [25][26][27][28][29] island evolution, 30,31 ordering and coarsening [19][20][21][32][33][34] as well as island growth on nanomembranes/nanoribbons. 35,36 Such continuum approaches give a long-wavelength description of the system, which has a large computational advantage over microscopic approaches but naturally neglects many microscopic crystalline details that can have a significant impact on film structural evolution and defect dynamics.…”